The compatibility problem is to find a figure that can be tiled with each of a set of polyforms. Here I show minimal known compatibility figures for the holey heptomino and other polyominoes. If you find a smaller solution or solve an unsolved case, please let me know.
Compatibility with trominoes, tetrominoes, and pentominoes was first solved by Giovanni Resta. You can see his work at his monumental website Polypolyominoes.
Thanks to Jenard Cabilao for suggesting this problem.
Last revised 2015-04-17.